Likelihood inference for spatial point processes

Abstract

This chapter deals with likelihood inference for spatial point processes using the methods of R. A. Moyeed and A. J. Baddeley, C. J. Geyer and E. A. Thompson, A. E. Gelfand and B. P. Carlin, C. J. Geyer, and C. J. Geyer and J. Moller using Markov chain Monte Carlo (MCMC). The MCMC, including the Gibbs sampler and the Metropolis, the Metropolis–Hastings, and the Metropolis–Hastings–Green algorithms, permits the simulation of any stochastic process specified by an unnormalized density. Thus the family of unnormalized densities is involved in both conditional likelihood inference and likelihood inference with missing data. Latent variables, random effects, and ordinary empirical Bayes models all involve missing data of some form. Missing data involve the same considerations as conditional families. The oldest general class of models specified by unnormalized densities are exponential families. Models specified by unnormalized densities present a problem for Bayesian inference.